Skip to main content

Standard curve database

Search

sect113r2

113-bit binary field Weierstrass curve.
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m113
f(u)u^113 + u^9 + 1
a0x00689918dbec7e5a0dd6dfc0aa55c7
b0x0095e9a9ec9b297bd4bf36e059184f
G(0x01a57a6a7b26ca5ef52fcdb8164797, 0x00b3adc94ed1fe674c06e695baba1d)
n0x010000000000000108789b2496af93
h0x2


Characteristics

  • OID:
    1.3.132.0.5
  • j-invariant:
    3925759440046949401308357014943784
  • Trace of Frobenius:
    -148884003161464613
  • Discriminant:
    3040591781815807764515357141309519

SAGE

F.<x> = GF(2)[]
K = GF(2^113, name="x", modulus=u^113 + u^9 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x00689918dbec7e5a0dd6dfc0aa55c7), 0, 0, K.from_integer(0x0095e9a9ec9b297bd4bf36e059184f)))
E.set_order(0x010000000000000108789b2496af93 * 0x2)
G = E(K.from_integer(0x01a57a6a7b26ca5ef52fcdb8164797), K.from_integer(0x00b3adc94ed1fe674c06e695baba1d))


JSON

{
"name": "sect113r2",
"desc": "",
"oid": "1.3.132.0.5",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 113,
"poly": [
{
"power": 113,
"coeff": "0x01"
},
{
"power": 9,
"coeff": "0x01"
},
{
"power": 0,
"coeff": "0x01"
}
],
"degree": 113,
"basis": "poly"
},
"params": {
"a": {
"raw": "0x00689918dbec7e5a0dd6dfc0aa55c7"
},
"b": {
"raw": "0x0095e9a9ec9b297bd4bf36e059184f"
}
},
"generator": {
"x": {
"raw": "0x01a57a6a7b26ca5ef52fcdb8164797"
},
"y": {
"raw": "0x00b3adc94ed1fe674c06e695baba1d"
}
},
"order": "0x010000000000000108789b2496af93",
"cofactor": "0x2",
"characteristics": {
"discriminant": "3040591781815807764515357141309519",
"j_invariant": "3925759440046949401308357014943784",
"trace_of_frobenius": "-148884003161464613"
}
}

© 2020-2025 Jan Jancar | Built with Dox theme for Gatsby